On the creations of critical points in scale space with applications to medical image analysis

Abstract

In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the various different types of annihilations and creations of pairs of spatial critical points and how this knowledge can be exploited in finding and tracing these points. We clarify the theory with an artifi- cial image and a simulated MR image.